Robots don’t care

I find it pretty much impossible to think about robots without thinking about AI and about all the speculations about the Singularity or this and that. Of course, we are all familiar with ideas of robots and AI either being unfeeling, uncaring, human-destroying psychopaths or the benevolent and servile to humanity AI. But these both seem to imply some sort of thought process based in our own biology.

What if intelligence that isn’t backed by billions of years of reproductive and self-preservation instinct just doesn’t care at all if it lives or dies or has a purpose or not?